Hi, I'm Mihai Cucuringu and I just finished my sophomore year at Hiram College, Ohio. This webpage contains the work I have done at the REU from Cornell University, during the summer of 2005.

I was in the "Analysis on Fractals" group and worked under Prof. Robert Strichartz on the Effective Resistance on the Sierpinski gasket and Self-Similar Energy Forms on the Sierpinski gasket with twists projects.

Since I am an International student and was not allowed to be paid with NSF funds, my research was supported by a partial grant from Hiram College and personal funds.

Here is an outline of what you will find on this website. Follow the menu on the left for more detailed information.

Effective Resistance Metric

Infinitesimal resistance, new self-similar resistance metric.

Dynamical System (1-dim) & uniqueness of the attracting fixed point

Dynamical System (3-dim). Attractor.

Effective Resistance at Periodic Points.

Resistances on whole gasket (SG, SG3, SG at periodic point)

Resistance Balls on SG & SG3. Pictures. Graph of Volumes and renormalized Volumes.

Generalization to p.c.f case with N ₀=3

Self-Similar Energies with Two Twists

Sabot's Initial Renormalization Problem

Two Twists Renormalization Problem

Geometric Model

Dynamical System

Analysis of the r1=r2 Case

Analysis of the Limit Case

Numerical Evidence & Surface of the Renormalization Factors.

Self-Similar Energies with Three Twists

Three Twists Renormalization Problem

Graphs of the Admissible Weights Surface (with MAPLE Code)

S-plane of Solutions (s₁, s₂) and Boundary Curves (with MAPLE Code)

Click here to download my final presentation for the Undergraduate Research Forum (Thursday, July 28, 2005)